I absolutely agree with anonaman. Tenure is not just about your research productivity, but also about your fit & value to the college or university. Furthermore, even a few years of a post-doc is pretty different than an assistant professor position. Most post-docs I know might teach a class or two, but they don't have the teaching load, advising responsibilities, service (dept, college & professional), and contribution to the field (independent of a mentor) that assistant professors usually have when going up for tenure.
At my interviews this possibility came up (of going up for tenure early) but everyone (the interviewing institutions and my mentors) have told me *absolutely* not to decide on that until I get to my new institution & get my feet wet. You can always go up early (and typically that's seen as a good thing) but if you negotiate for a shorter clock and then find the adjustment/balancing tougher than you thought — well, then you're really in a pickle. Going up early looks a lot better than negotiating for a shorter clock and then backing down on that. Even if you still just did the typical timeline, it would reflect poorly on you, I think.
The other thing I'll add is that I think sometimes we're so focused on getting the tenure-track job that we forget that it's really, really hard to move after tenure. The tenure-track is also an opportunity for YOU to decide whether you want to be there for a very, very long time. It's like a marriage, kind of, and the tenure-track is like the dating or engagement period! A colleague of mine is in this situation now. He's tenured at a great institution, but has married later in life and his spouse lives a few hours away. (The spouse is also an academic, but is less move-able because the spouse has a big lab with grad students, post-docs, relies on some specialty resources at this univ, etc.) My colleague is trying to find another position closer to the spouse but he (a) doesn't want to live too far apart from his spouse, and (b) doesn't want to have to re-do tenure. He has inquired at many institutions and gotten a few bites, but no wants wants to hire at the associate level.